CN110763328B - Half-space sound field reconstruction method and device - Google Patents

Half-space sound field reconstruction method and device Download PDF

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CN110763328B
CN110763328B CN201911124723.1A CN201911124723A CN110763328B CN 110763328 B CN110763328 B CN 110763328B CN 201911124723 A CN201911124723 A CN 201911124723A CN 110763328 B CN110763328 B CN 110763328B
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sound field
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CN110763328A (en
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景文倩
刘广胜
聂金泉
吴华为
丁华锋
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Hubei University of Arts and Science
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    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H17/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves, not provided for in the preceding groups
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H1/00—Measuring characteristics of vibrations in solids by using direct conduction to the detector
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Abstract

The invention discloses a half-space sound field reconstruction method and a half-space sound field reconstruction device, wherein the method comprises the following steps: configuring equivalent sources and virtual source surfaces according to the vibrating body and the boundary surface to obtain a plurality of equivalent source configuration schemes; aiming at each equivalent source configuration scheme, calculating a regular solution of a source strong column vector corresponding to each equivalent source configuration scheme based on the predicted sound pressure of the half-space sound field; reconstructing the surface normal vibration speed of the vibrator corresponding to each equivalent source configuration scheme based on the regular solution of the source strong column vector, and further calculating the reconstruction error of the surface normal vibration speed of the vibrator; and finally, the equivalent source configuration scheme with the minimum reconstruction error of the normal vibration speed of the surface of the vibrator is used as a final equivalent source configuration scheme to reconstruct a half-space sound field. The invention utilizes the half-space near-field acoustic holography technology, ensures the reconstruction precision of a half-space sound field by reasonably configuring equivalent sources, does not depend on the surface acoustic impedance of a reflecting surface, and has lower measurement cost.

Description

Half-space sound field reconstruction method and device
Technical Field
The invention relates to the technical field of physical acoustics, in particular to a half-space sound field reconstruction method and device based on a half-space near-field acoustic holography technology.
Background
When the vibrating body is located in a half-space sound field environment with a boundary, the influence of the reflection action of the boundary on the sound field is generally considered. The field separation technique can be used to reconstruct a half-space field because it can separate the input sound and the output sound, and has a distinct advantage in that it does not require knowledge of the surface acoustic impedance of the reflecting surface. However, this technique requires that the measuring surface must be a closed surface that envelopes the vibrating body to ensure that the reflected sound propagates into the half-space sound field to be studied just from the other side of the measuring surface. In addition, the sound field separation technology itself has many requirements on the measurement surface, such as double-sided sound pressure measurement or double-sided particle vibration velocity measurement, or single-sided sound pressure-particle vibration velocity measurement. This results in high measurement costs, including economic costs for the measurement equipment and the like and measurement working time costs.
If the surface acoustic impedance of the reflecting surface is known, a half-space Green function can be introduced into the traditional near-field acoustic holography technology to realize reconstruction of a half-space sound field. There are currently two types of semi-spatial green functions: one is based on the assumption of plane waves, and the reflected sound waves are considered to be the plane waves, so that the reconstruction precision of a half-space sound field is obviously reduced when the distance between a vibrating body and a reflecting surface is not far enough; and the other type of the method is based on real spherical waves, automatically meets the boundary conditions of a reflecting surface, can obtain high reconstruction precision of a half-space sound field, and is time-consuming in calculation due to integration. In addition, this method requires a priori knowledge of the acoustic impedance of the reflecting surface, i.e. a dependence on the surface acoustic impedance of the reflecting surface.
There is a technique of half-space near-field acoustic holography that neither requires a priori knowledge of the surface acoustic impedance of the reflecting surface nor a high measurement cost, because this method equates the reflected sound produced by the reflecting surface to a series of radiated sounds from a simple source located below the reflecting surface. At the moment, the problem of a half-space sound field is converted into the problem of a multi-source free sound field, the surface acoustic impedance of a reflecting surface does not need to be considered, and only single-side sound pressure or particle vibration velocity is needed for measurement, so that the measurement cost is greatly reduced. This Method is called I-ESM (Independent-Equivalent Source Method) because it does not depend on the surface acoustic impedance of the reflecting surface and is based on the Equivalent Source Method. The reconstruction accuracy of the I-ESM half-space sound field depends to a great extent on the configuration of the equivalent sources, especially the series of equivalent sources that characterize the action of the reflecting surfaces. Thus, unreasonable equivalent source configurations may significantly degrade the half-space soundfield reconstruction accuracy of the I-ESM.
Therefore, the existing half-space sound field reconstruction method has three defects and shortcomings: (1) the measurement cost is high; (2) surface acoustic impedance dependent on the reflecting surface; (3) the reconstruction accuracy is not ideal.
Disclosure of Invention
The invention aims to provide a half-space sound field reconstruction method and device by utilizing a half-space near-field acoustic holography technology, which ensure the reconstruction precision of a half-space sound field by reasonably configuring an equivalent source, are independent of the surface acoustic impedance of a reflecting surface and have lower measurement cost.
The technical scheme adopted by the invention is as follows:
in one aspect, the present invention provides a half-space sound field reconstruction method, including:
configuring equivalent sources and virtual source surfaces according to the vibrating body and the boundary surface to obtain a plurality of equivalent source configuration schemes; the virtual source surface comprises a virtual source surface gamma where the vibrating body equivalent source is located and a virtual source surface omega where the boundary surface reflection action equivalent source is located;
respectively calculating sound pressure of a half-space sound field aiming at each equivalent source configuration scheme;
calculating a regular solution of source strong column vectors corresponding to each equivalent source configuration scheme based on the sound pressure of the half-space sound field;
reconstructing the surface normal vibration velocity of the vibrator corresponding to each equivalent source configuration scheme based on the regular solution of the source strong column vector;
calculating the reconstruction error of the surface normal vibration speed of the vibrating body of each equivalent source configuration scheme;
taking the equivalent source configuration scheme with the minimum reconstruction error of the normal vibration speed of the surface of the vibrator as a final equivalent source configuration scheme;
and reconstructing a half-space sound field by using the final equivalent source configuration scheme.
Optionally, the equivalent source configuration is performed according to the position and size of the virtual source surface and the distribution interval of the equivalent sources on the virtual source surface, so as to obtain a plurality of equivalent source configuration schemes.
Optionally, the vibrating body is spherical, and is defined as a spherical sound source S, and the equivalent source configuration includes:
configuring an imaginary source plane gamma as a spherical surface concentric with the spherical sound source S;
configuring the spherical radius of an imaginary source plane gamma;
configuring the distribution of a plurality of equivalent sources of the spherical sound source S on an imaginary source plane gamma;
configuring an imaginary source plane omega as a plane parallel to the reflecting surface;
the retreating distance of the virtual source surface omega relative to the reflecting surface is configured;
configuring the size of a virtual source surface omega;
the distribution of a plurality of equivalent sources characterizing the reflection of the reflecting surface over the imaginary source plane omega is configured.
As an embodiment, when the equivalent source is configured: a plurality of equivalent sources of the spherical sound source S are uniformly distributed on the virtual source plane gamma, and the discrete intervals of the azimuth angle and the polar angle of the equivalent sources on the virtual source plane gamma are pi/4 and pi/6; the size of the virtual source plane Ω is configured, that is, the coordinate range covered by the virtual source plane Ω on the abscissa and the ordinate is configured, and the distribution of the equivalent sources on the virtual source plane Ω is configured, that is, the interval between the equivalent sources in the directions of the abscissa and the ordinate is configured.
Optionally, the size of the virtual source plane Ω and the configuration of the equivalent source distribution are set by a parameter set (x)1,x2,y1,y2,dx,dy) Is represented by the formula (I) in which x1,x2Is the boundary value of the coordinate range covered by the imaginary source plane omega on the abscissa, y1,y2Is the boundary value of the coordinate range covered by the imaginary source plane omega on the ordinate, dx,dyThe discrete distances of the equivalent source on the imaginary source plane omega in the abscissa and ordinate directions.
Optionally, two groups of equivalent sources for characterizing the spherical sound source and the boundary reflection action are defined as
Figure GDA0003157766200000031
And
Figure GDA0003157766200000032
wherein
Figure GDA0003157766200000033
And
Figure GDA0003157766200000034
the source strengths of the ith and j equivalent sources respectively;
for any equivalent source configuration scheme, the matrix form of the sound pressure of the half-space sound field of all the measurement points on the holographic surface H is considered as follows:
Figure GDA0003157766200000035
wherein the content of the first and second substances,
Figure GDA0003157766200000036
is a sound pressure transfer function matrix between sound pressure on a representation holographic surface H and an equivalent source on an imaginary source surface gamma,
Figure GDA0003157766200000037
is a sound pressure transfer function matrix between sound pressure on a representation holographic surface H and an equivalent source on an imaginary source surface omega,
Figure GDA0003157766200000038
is a complex acoustic pressure transfer function matrix, QΣIs the source intensity column vector of all equivalent sources, i represents the imaginary unit, ρ represents the air density, and ω represents the angular frequency.
Optionally, the source strong column vector QΣThe canonical solution of (a) is:
Figure GDA0003157766200000039
wherein, the superscript "H" represents the Hermite conjugate transpose, the superscript "-1" represents the matrix inversion, ε represents the regularization parameter, and E is the identity matrix.
Optionally, the normal vibration speed V of the surface of the vibrating bodySThe reconstruction is as follows:
Figure GDA0003157766200000041
wherein the content of the first and second substances,
Figure GDA0003157766200000042
the vibration velocity transfer function matrix between the normal vibration velocity on the surface S of the vibration body and equivalent sources on virtual source surfaces gamma and omega is expressed as:
Figure GDA0003157766200000043
in the formula (I), the compound is shown in the specification,
Figure GDA0003157766200000044
consisting of the following functions:
Figure GDA0003157766200000045
Figure GDA0003157766200000046
consisting of the following functions:
Figure GDA0003157766200000047
in the formula, gv,free() Representing the particle velocity transfer function, k is the wave number, ". represents the dot product operation, nSIs the unit normal vector of the surface of the vibrating body,
Figure GDA0003157766200000048
is the nth node of the surface of the vibration body
Figure GDA00031577662000000427
With the ith equivalent source on the imaginary source plane gamma
Figure GDA0003157766200000049
The distance between the two or more of the two or more,
Figure GDA00031577662000000410
is that
Figure GDA00031577662000000411
With the j-th equivalent source on the virtual source plane omega
Figure GDA00031577662000000412
The distance between them;
Figure GDA00031577662000000413
representing equivalent sources
Figure GDA00031577662000000414
To surface node of vibration body
Figure GDA00031577662000000415
Linear transfer method ofThe included angle between the direction of the vibrator and the normal direction of the surface of the vibrator,
Figure GDA00031577662000000416
representing equivalent sources
Figure GDA00031577662000000417
To surface node of vibration body
Figure GDA00031577662000000418
The linear transmission direction of the vibrating body and the normal direction of the surface of the vibrating body form an included angle;
Figure GDA00031577662000000419
are respectively expressed as
Figure GDA00031577662000000420
Figure GDA00031577662000000421
Figure GDA00031577662000000422
Optionally, for any equivalent source configuration scheme, the reconstruction error of the surface normal vibration speed of the vibrating body is as follows:
Figure GDA00031577662000000423
in the formula (I), the compound is shown in the specification,
Figure GDA00031577662000000424
and
Figure GDA00031577662000000425
respectively is the reconstructed normal vibration speed and the theoretical normal vibration speed of the surface of the vibrator; the theoretical normal vibration velocity is expressed as:
Figure GDA00031577662000000426
in the formula, v0Is a uniform radial vibration velocity raIs the radius of the vibrating ball, zSIs the z coordinate of the surface node of the vibrating sphere, zaIs the z coordinate of the center of the sphere.
On the other hand, the invention also discloses a half-space sound field reconstruction device, which comprises:
the equivalent source configuration module is used for configuring equivalent sources and virtual source surfaces according to the vibrating body and the boundary surface to obtain a plurality of equivalent source configuration schemes; the virtual source surface comprises a virtual source surface gamma where the vibrating body equivalent source is located and a virtual source surface omega where the boundary surface reflection action equivalent source is located;
the source intensity column vector regular solution calculation module is used for calculating the regular solution of the source intensity column vector corresponding to each equivalent source configuration scheme based on the predicted sound pressure of the half-space sound field aiming at each equivalent source configuration scheme;
the vibrating body surface normal vibration velocity calculating module is used for reconstructing the vibrating body surface normal vibration velocity corresponding to each equivalent source configuration scheme based on the regular solution of the source strong column vector;
the reconstruction error calculation module is used for calculating the reconstruction errors of the surface normal vibration speeds of the vibrating bodies of the equivalent source configuration schemes;
the equivalent source configuration scheme selection module is used for taking the equivalent source configuration scheme with the minimum reconstruction error of the normal vibration velocity of the surface of the vibrating body as a final equivalent source configuration scheme;
and the half-space sound field reconstruction module is used for reconstructing the half-space sound field by utilizing the final equivalent source configuration scheme.
Advantageous effects
According to the method, equivalent source configuration is carried out on the basis of a half-space near-field acoustic holography technology I-ESM, the reconstruction error of the normal vibration speed of the surface of the vibrating body is taken as a reference, and the scheme with the minimum reconstruction error is selected from a plurality of equivalent source configuration schemes, so that the proper virtual source surface position, the virtual source surface size and the equivalent source distribution interval are determined, the half-space sound field is reconstructed, the influence of a reflecting surface on the half-space sound field can be more accurately represented, the reconstruction precision of the half-space sound field is improved, and the reconstruction precision of the half-space sound field is improved. Meanwhile, by utilizing the semi-space near-field acoustic holography technology, the semi-space sound field problem is converted into a multi-source free sound field problem, the surface acoustic impedance of a reflecting surface does not need to be considered, and only single-side sound pressure or particle vibration velocity is needed for measurement, so that the measurement cost can be greatly reduced.
Drawings
FIG. 1 is a schematic flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of the relative positions of a spherical sound source S, a holographic surface H, virtual source surfaces Γ and Ω in three-dimensional space according to an embodiment of the method of the present invention;
fig. 3 is a plan view of a spherical sound source S, a holographic surface H, and an imaginary source surface Ω, and the size and equivalent source distribution interval of the imaginary source surface Ω in an embodiment of the method of the present invention, (a) a top view; (b) a side view;
FIG. 4 shows different equivalent source configurations (parameter set (x)) in an embodiment of the method of the present invention1,x2,y1,y2,dx,dy) And a receding distance hz) Under the condition of 500Hz, reconstructing errors of the normal vibration speed of the surface of the spherical sound source;
FIG. 5 is a diagram of the geometry of an imaginary source plane Ω in an embodiment of the method of the present invention, (a) a square; (b) a rectangle shape;
FIG. 6 shows the reconstructed result and theoretical value of the normal vibration velocity of the spherical sound source surface at 500Hz in the embodiment of the method of the present invention, (a) the real part; (b) x is a theoretical value; from parameter set number 15 and hz-0.001 m; from parameter set 1 and hz-0.2m of the obtained reconstruction;
Figure GDA0003157766200000061
from parameter set No. 6 and hz-0.5m of the obtained reconstruction;
FIG. 7 is a spherical sound source surface normal vibration velocity reconstruction error frequency response curve in an embodiment of the method of the present invention;
FIG. 8 is a graph showing the variation of the reconstruction error of the normal vibration velocity of the surface of the spherical sound source with the flow resistance of the reflecting surface at 500Hz in the embodiment of the method of the present invention.
Detailed Description
The following further description is made in conjunction with the accompanying drawings and the specific embodiments.
Example 1
Referring to fig. 1, the half-space sound field reconstruction method of the present embodiment includes:
configuring equivalent sources and virtual source surfaces according to the vibrating body and the boundary surface to obtain a plurality of equivalent source configuration schemes; the virtual source surface comprises a virtual source surface gamma where the vibrating body equivalent source is located and a virtual source surface omega where the boundary surface reflection action equivalent source is located;
respectively calculating sound pressure of a half-space sound field aiming at each equivalent source configuration scheme;
calculating a regular solution of source strong column vectors corresponding to each equivalent source configuration scheme based on the sound pressure of the half-space sound field;
reconstructing the surface normal vibration velocity of the vibrator corresponding to each equivalent source configuration scheme based on the regular solution of the source strong column vector;
calculating the reconstruction error of the surface normal vibration speed of the vibrating body of each equivalent source configuration scheme;
taking the equivalent source configuration scheme with the minimum reconstruction error of the normal vibration speed of the surface of the vibrator as a final equivalent source configuration scheme;
and reconstructing a half-space sound field by using the final equivalent source configuration scheme.
In this embodiment, equivalent source configuration is performed according to the position and size of the virtual source surface and the distribution interval of the equivalent sources on the virtual source surface, so as to obtain a plurality of equivalent source configuration schemes.
If the vibrating body is spherical, defined as a spherical sound source S, the equivalent source configuration includes:
configuring an imaginary source plane gamma as a spherical surface concentric with the spherical sound source S;
configuring the spherical radius of an imaginary source plane gamma;
configuring the distribution of a plurality of equivalent sources of the spherical sound source S on an imaginary source plane gamma;
configuring an imaginary source plane omega as a plane parallel to the reflecting surface;
the retreating distance of the virtual source surface omega relative to the reflecting surface is configured;
configuring the size of a virtual source surface omega;
the distribution of a plurality of equivalent sources characterizing the reflection of the reflecting surface over the imaginary source plane omega is configured.
When the equivalent source is configured: a plurality of equivalent sources of the spherical sound source S are uniformly distributed on the virtual source plane gamma, and the discrete intervals of the azimuth angle and the polar angle of the equivalent sources on the virtual source plane gamma are pi/4 and pi/6; the size of the virtual source plane Ω is configured, that is, the coordinate range covered by the virtual source plane Ω on the abscissa and the ordinate is configured, and the distribution of the equivalent sources on the virtual source plane Ω is configured, that is, the interval between the equivalent sources in the directions of the abscissa and the ordinate is configured.
The size of the virtual source plane omega and the configuration of the equivalent source distribution are set by the parameter set (x)1,x2,y1,y2,dx,dy) Is represented by the formula (I) in which x1,x2Is the boundary value of the coordinate range covered by the imaginary source plane omega on the abscissa, y1,y2Is the boundary value of the coordinate range covered by the imaginary source plane omega on the ordinate, dx,dyThe discrete distances of the equivalent source on the imaginary source plane omega in the abscissa and ordinate directions.
Two groups of equivalent sources for representing the effects of spherical sound sources and boundary reflection are respectively defined as
Figure GDA0003157766200000071
And
Figure GDA0003157766200000072
wherein
Figure GDA0003157766200000073
And
Figure GDA0003157766200000074
the source strengths of the ith and j equivalent sources respectively;
for any equivalent source configuration scheme, the matrix form of the sound pressure of the half-space sound field of all the measurement points on the holographic surface H is considered as follows:
Figure GDA0003157766200000081
wherein the content of the first and second substances,
Figure GDA0003157766200000082
is a sound pressure transfer function matrix between sound pressure on a representation holographic surface H and an equivalent source on an imaginary source surface gamma,
Figure GDA0003157766200000083
is a sound pressure transfer function matrix between sound pressure on a representation holographic surface H and an equivalent source on an imaginary source surface omega,
Figure GDA0003157766200000084
is a complex acoustic pressure transfer function matrix, QΣIs the source intensity column vector of all equivalent sources, i represents the imaginary unit, ρ represents the air density, and ω represents the angular frequency.
Source strong column vector QΣThe canonical solution of (a) is:
Figure GDA0003157766200000085
wherein, the superscript "H" represents the Hermite conjugate transpose, the superscript "-1" represents the matrix inversion, ε represents the regularization parameter, and E is the identity matrix.
Normal vibration speed V of surface of vibratorSThe reconstruction is as follows:
Figure GDA0003157766200000086
wherein the content of the first and second substances,
Figure GDA0003157766200000087
the vibration velocity transfer function matrix between the normal vibration velocity on the surface S of the vibration body and equivalent sources on virtual source surfaces gamma and omega is expressed as:
Figure GDA0003157766200000088
in the formula (I), the compound is shown in the specification,
Figure GDA0003157766200000089
consisting of the following functions:
Figure GDA00031577662000000810
Figure GDA0003157766200000091
consisting of the following functions:
Figure GDA0003157766200000092
in the formula, gv,free() Representing the particle velocity transfer function, k is the wave number, ". represents the dot product operation, nSIs the unit normal vector of the surface of the vibrating body,
Figure GDA0003157766200000093
is the nth node of the surface of the vibration body
Figure GDA0003157766200000094
With the ith equivalent source on the imaginary source plane gamma
Figure GDA0003157766200000095
The distance between the two or more of the two or more,
Figure GDA0003157766200000096
is that
Figure GDA0003157766200000097
With the j-th equivalent source on the virtual source plane omega
Figure GDA0003157766200000098
The distance between them;
Figure GDA0003157766200000099
representing equivalent sources
Figure GDA00031577662000000910
To surface node of vibration body
Figure GDA00031577662000000911
The included angle between the straight line transmission direction and the normal direction of the surface of the vibrating body,
Figure GDA00031577662000000912
representing equivalent sources
Figure GDA00031577662000000913
To surface node of vibration body
Figure GDA00031577662000000914
The linear transmission direction of the vibrating body and the normal direction of the surface of the vibrating body form an included angle;
Figure GDA00031577662000000915
are respectively expressed as
Figure GDA00031577662000000916
Figure GDA00031577662000000917
Figure GDA00031577662000000918
For any equivalent source configuration scheme, the reconstruction error of the surface normal vibration speed of the vibrating body is as follows:
Figure GDA00031577662000000919
in the formula (I), the compound is shown in the specification,
Figure GDA00031577662000000920
and
Figure GDA00031577662000000921
respectively the reconstructed normal vibration speed and theory of the surface of the vibratorNormal vibration speed; the theoretical normal vibration velocity is expressed as:
Figure GDA00031577662000000922
in the formula, v0Is a uniform radial vibration velocity raIs the radius of the vibrating ball, zSIs the z coordinate of the surface node of the vibrating sphere, zaIs the z coordinate of the center of the sphere.
Examples 1 to 2
Based on embodiment 1, in this embodiment, a spherical sound source S with a radius of 0.1m is located above a certain reflection surface as an example, and a half-space sound field is reconstructed.
A Cartesian rectangular coordinate system is established by taking the projection of the circle center of the spherical sound source S on the reflecting surface as an origin and the reflecting surface as an xOy plane, and the sound field with z larger than 0 is a half-space sound field to be researched. Assume that the spherical center of the spherical sound source S is 0.5m from the reflection surface, as shown in fig. 3 (b). The spherical sound source S is taken as a simulation object for research, and the method for reconstructing the half-space sound field comprises the following specific steps:
step A: two groups of equivalent sources representing the reflection action of the spherical sound source S and the boundary surface are respectively arranged on an imaginary source surface gamma and an imaginary source surface omega, which are respectively marked as
Figure GDA0003157766200000101
And
Figure GDA0003157766200000102
wherein
Figure GDA0003157766200000103
And
Figure GDA0003157766200000104
the source strengths of the ith and j equivalent sources, respectively. The virtual source plane gamma is a small spherical surface concentric with the spherical sound source S, the spherical radius is 0.02m, and the equivalent source Q isΓUniformly distributed over the virtual source plane Γ, at discrete intervals of π/4 and π/6, respectively, in azimuth and polar angles. The imaginary source plane omega is a plane parallel to the reflecting surface, as shown in FIG. 2, the equivalent source QΩIs prepared fromThe placement scheme may be considered from two aspects: (1) the position of the virtual source plane omega is set by a back distance h relative to the reflecting surfacezRepresents; (2) size of virtual source plane, equivalent source distribution interval, etc., in a parameter set (x)1,x2,y1,y2,dx,dy) As shown in fig. 3. Wherein the retreat distance hzSequentially setting the grain size to be-0.001 m, -0.2m, -0.5m and-1 m; parameter set (x)1,x2,y1,y2,dx,dy) There were 22 sets as shown in table 1.
Table 122 sets of equivalent source configuration parameters (x)1,x2,y1,y2,dx,dy)
Figure GDA0003157766200000105
And B: selecting an equivalent source QΓAnd QΩIn one configuration, the sound pressure at a certain point r on the holographic surface H can be expressed as:
Figure GDA0003157766200000106
where ρ is the air density, ω is the angular frequency,
Figure GDA0003157766200000107
and
Figure GDA0003157766200000108
the position coordinates of the ith and the j equivalent sources in the three-dimensional space respectively. gfreeRepresenting the free space green's function, the sound pressure transfer function, can be expressed as:
Figure GDA0003157766200000111
wherein, k is a wave number,
Figure GDA0003157766200000112
is the field point r and the equivalent source point
Figure GDA0003157766200000113
The distance of (a) to (b),
Figure GDA0003157766200000114
is the horizontal distance between the two.
Assuming that the hologram surface H has M measurement points, considering all the measurement points on the hologram surface H, equation (1) can be written in a matrix form:
Figure GDA0003157766200000115
in the formula (I), the compound is shown in the specification,
Figure GDA0003157766200000116
is a sound pressure transfer function matrix between sound pressure on a representation holographic surface H and an equivalent source on an imaginary source surface gamma,
Figure GDA0003157766200000117
is a sound pressure transfer function matrix between sound pressure on a representation holographic surface H and an equivalent source on an imaginary source surface omega,
Figure GDA0003157766200000118
is a complex acoustic pressure transfer function matrix, QΣIs the source strong column vector of all equivalent sources.
In the present embodiment, the hologram surface H is located at a position where y is 0.2m, the measurement range is-0.25 m to 0.25m in the x direction, 0.25m to 0.75m in the z direction, and the measurement interval is 0.05 m. The holographic sound pressure data can be directly measured in practical application; if the numerical simulation calculation is carried out, the numerical simulation calculation is generally carried out by a boundary element method, and Gaussian white noise with the signal-to-noise ratio of 30dB is added.
And C: on condition that the number of measurement points is greater than the number of equivalent sources, i.e. M>I + J, based on holographic sound pressure PHSolving for the equivalent source QΣThe canonical solution of (c):
Figure GDA0003157766200000119
the upper mark in the formula: "H" represents the Hermite conjugate transpose, "-1" represents the matrix inversion operation, and epsilon is the regularization parameter; e is an identity matrix.
Step D: obtaining an equivalent source QΣAfter the regular solution, the normal vibration speed of the surface of the vibrating body can be reconstructed:
Figure GDA0003157766200000121
in the formula,
Figure GDA0003157766200000122
is a vibration velocity transfer function matrix between the normal vibration velocity on the surface S of the vibration body and equivalent sources on virtual source surfaces gamma and omega,
Figure GDA0003157766200000123
can be expressed as:
Figure GDA0003157766200000124
in the formula (I), the compound is shown in the specification,
Figure GDA0003157766200000125
and
Figure GDA0003157766200000126
respectively consisting of the following functions:
Figure GDA0003157766200000127
Figure GDA0003157766200000128
wherein ". cndot." represents a dot product fortuneN is calculatedSIs the unit normal vector of the surface of the vibrating body,
Figure GDA0003157766200000129
is the nth node of the surface of the vibration body
Figure GDA00031577662000001210
And
Figure GDA00031577662000001211
the distance between the two or more of the two or more,
Figure GDA00031577662000001212
is that
Figure GDA00031577662000001213
And
Figure GDA00031577662000001214
the distance between them.
Step E: calculating the reconstruction error of the surface normal vibration speed of the vibrating body:
Figure GDA00031577662000001215
in the formula (I), the compound is shown in the specification,
Figure GDA00031577662000001216
and
Figure GDA00031577662000001217
the reconstructed normal vibration velocity and the theoretical normal vibration velocity of the surface of the vibrating body are respectively.
Figure GDA00031577662000001218
Expressed as:
Figure GDA00031577662000001219
in the formula, v0Is a uniform radial vibration velocity raIs the radius of the vibrating ball，zSIs the z coordinate of the surface node of the vibrating sphere, zaIs the z coordinate of the center of the sphere. In numerical simulation, the theoretical normal vibration velocity
Figure GDA00031577662000001220
The theoretical normal vibration velocity can be obtained from the formula (10), and can be obtained through measurement in practical application.
Step F: sequentially selecting equivalent sources QΓAnd QΩAnd (e) repeating the steps b to e, analyzing and comparing the reconstruction errors of the normal vibration speed of the surface of the vibrator under the conditions of different configuration schemes, and searching for a smaller value, wherein the corresponding equivalent source configuration scheme is the more appropriate equivalent source configuration scheme in the half-space sound field.
FIG. 4 shows the spherical sound source surface normal vibration velocity reconstruction error at 500Hz under different equivalent source configurations in the embodiment of the method of the present invention.
First, the retreat distance h is analyzedz. At hzUnder the conditions of sequentially taking the values of-0.001 m, -0.2m and-0.5 m, the parameter group (x)1,x2,y1,y2,dx,dy) When the values are the same, the reconstruction error of the normal vibration velocity follows hzIs reduced. But when h iszWhen the value is smaller-1 m, the reconstruction error is not reduced any more, but sometimes increased. As a result, a receding distance h of-0.5 m was obtainedzIt is a more ideal choice. Interestingly, the spherical sound source S is located just 0.5m above the reflecting surface. Therefore, the back-off distance of the imaginary source plane Ω with respect to the reflecting surface should be comparable to the distance of the sound source above the reflecting surface in order to obtain better half-space sound field reconstruction results.
Next, the size (x) of the virtual source plane Ω is analyzed1,x2,y1,y2) And an equivalent source distribution interval (d)x,dy). When h is generatedzWhen the values are-0.001 m, -0.2m, -0.5m, especially when the first two values are taken, each normal vibration velocity reconstruction error curve has the same turning point, such as No. 3 and No. 17. With reference to Table 1, these turning points are exactly the size (x) of the virtual source plane Ω1,x2,y1,y2) Changed situation. In addition, when the magnitude of the virtual source plane Ω is the same, the reconstruction error is spaced with the equivalent source distribution (d)x,dy) The variation is not large. Therefore, the size of the virtual source plane omega has a relatively obvious influence on the reconstruction accuracy, and the equivalent source distribution interval has a very small influence on the reconstruction accuracy. But when h iszWhen the value is-1 m, that is, when the virtual source plane Ω is far from the reflecting surface, the reconstruction accuracy is hardly affected by the size or the equivalent source distribution interval. In view of the above analysis results, to simplify the analysis process, only the equivalent source distribution interval (d) is analyzed belowx,dy) All 0.05 m.
Then, the special points are analyzed. When h is generatedz0.001m or hzWhen the normal vibration velocity is equal to-0.2 m, the reconstruction error of the normal vibration velocity is respectively in the parameter group (x)1,x2,y1,y2,dx,dy) The minimum value and the maximum value are taken for the 9 th and the 15 th. With reference to table 1 and fig. 5, the virtual source plane Ω 9 determined by the parameter set No. 9 exactly covers the area between the sound source and the hologram plane, and the virtual source plane Ω 15 determined by the parameter set No. 15 is the largest virtual source plane covering the area determined by all the parameter sets. These analysis results show that in the case where the virtual source plane is relatively close to the reflection plane, such as-0.001 m and-0.2 m, the equivalent source should be arranged in the region between the sound source and the hologram plane.
Finally, the best equivalent source configuration is found. From the above analysis, the retreat distance hzShould be set to-0.5 m, but if the parameter set (x)1,x2,y1,y2,dx,dy) When the selection is improper, the error of the normal vibration velocity reconstruction may be slightly larger, sometimes even larger than h under the condition of the same parameter groupzTake the reconstruction error at-1 m, say # 15. As can be seen from FIG. 4, at hzIn the case of-0.5 m, when the parameter set is No. 3, No. 6, No. 9, No. 11, or No. 20, the reconstruction error is small. As can be seen from fig. 5(a), Ω 3 exactly covers the projection of the spherical sound source on the virtual source plane Ω; omega 6 is slightly smaller, and equivalent sources are all focused on the projection of the central part of the spherical sound source on omega; omega 20 also covers the projection of the central part of the spherical sound source on omega. On the other hand, Ω 9 just covers soundThe region between the source and the holographic surface, Ω 11, although slightly larger, covers this region too, and in any case, in order to obtain a better reconstruction result, the virtual source surface Ω should cover either the projection of the central part of the spherical sound source on Ω or the region between the sound source and the holographic surface, and the virtual source surface should not be oversized.
Based on the above analysis, table 2 gives 3 representative equivalent source configurations.
TABLE 2 equivalent source configuration scheme and corresponding normal vibration velocity reconstruction error
Figure GDA0003157766200000141
Wherein, the 15 th parameter group (x)1,x2,y1,y2,dx,dy) And hz-0.001m represents a poor solution, parameter set No. 6 and hz-0.5m represents a better solution, while parameter set No. 1 and hzA value of-0.2 m is neither too good nor too bad. The spherical sound source surface normal vibration velocity is reconstructed by respectively adopting 3 equivalent source configuration schemes, and the reconstruction result is shown in fig. 6. As can be seen from the figure, the sum h is given by parameter set No. 6zThe reconstruction results obtained at-0.5 m fit very well with the theoretical values, and are given by the parameter set No. 15 and hzThe reconstruction results obtained at-0.001 m deviate considerably from the theoretical values. In addition, table 2 also shows the reconstruction error of the normal vibration velocity in the case of three equivalent source configurations. It can be easily found thatzThe reconstruction error obtained for-0.5 m is small, and is given by parameter set No. 15 and hzThe reconstruction error obtained is much larger at-0.001 m. These analysis results show parameter set No. 6 and hzThe equivalent source configuration scheme is relatively suitable, and the I-ESM is an effective high-precision half-space sound field reconstruction method as long as the equivalent source configuration is reasonable.
In addition, fig. 7 and 8 show the variation curves of the spherical sound source surface normal vibration velocity reconstruction error along with the frequency and the flow resistance of the reflecting surface respectively. As can be seen from the figure, the sum of the parameter set No. 6 and the parameter set hzReconstruction error obtained at-0.5 mThe difference is always small, and is composed of parameter set No. 15 and hzThe reconstruction error obtained is much larger at-0.001 m, and parameter set No. 6 and h will be explained againzAn ideal equivalent source configuration scheme is-0.5 m, and a suitable equivalent source configuration scheme can provide higher and more stable half-space sound field reconstruction accuracy for I-ESM.
In summary, the analysis results of the examples fully illustrate that: (1) the invention can provide a proper equivalent source configuration scheme that the retreat distance of the virtual source surface omega relative to the reflecting surface is equivalent to the distance of the sound source above the reflecting surface, and omega covers the projection of the central part of the spherical sound source on omega or the area between the sound source and the holographic surface, and the size is not suitable to be overlarge; (2) the appropriate equivalent source configuration scheme obtained by the method can ensure the accuracy of the semi-space near-field acoustic holography technology I-ESM which does not depend on the surface impedance of the reflecting surface and has low measurement cost, provides higher and more stable semi-space sound field reconstruction precision for the I-ESM, and verifies the beneficial effects of the method.
Example 2
Based on the same inventive concept as the embodiment, the embodiment is a half-space sound field reconstruction apparatus, including:
the equivalent source configuration module is used for configuring equivalent sources and virtual source surfaces according to the vibrating body and the boundary surface to obtain a plurality of equivalent source configuration schemes; the virtual source surface comprises a virtual source surface gamma where the vibrating body equivalent source is located and a virtual source surface omega where the boundary surface reflection action equivalent source is located;
the source intensity column vector regular solution calculation module is used for calculating the regular solution of the source intensity column vector corresponding to each equivalent source configuration scheme based on the predicted sound pressure of the half-space sound field aiming at each equivalent source configuration scheme;
the vibrating body surface normal vibration velocity calculating module is used for reconstructing the vibrating body surface normal vibration velocity corresponding to each equivalent source configuration scheme based on the regular solution of the source strong column vector;
the reconstruction error calculation module is used for calculating the reconstruction errors of the surface normal vibration speeds of the vibrating bodies of the equivalent source configuration schemes;
the equivalent source configuration scheme selection module is used for taking the equivalent source configuration scheme with the minimum reconstruction error of the normal vibration velocity of the surface of the vibrating body as a final equivalent source configuration scheme;
and the half-space sound field reconstruction module is used for reconstructing the half-space sound field by utilizing the final equivalent source configuration scheme.
The specific functions of the above modules are implemented with reference to embodiment 1.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (10)

1. A half-space sound field reconstruction method is characterized by comprising the following steps:
configuring equivalent sources and virtual source surfaces according to the vibrating body and the boundary surface to obtain a plurality of equivalent source configuration schemes; the virtual source surface comprises a virtual source surface gamma where the vibrating body equivalent source is located and a virtual source surface omega where the boundary surface reflection action equivalent source is located;
aiming at each equivalent source configuration scheme, respectively calculating a regular solution of a source strong column vector corresponding to each equivalent source configuration scheme based on the predicted sound pressure of the half-space sound field;
reconstructing the surface normal vibration velocity of the vibrator corresponding to each equivalent source configuration scheme based on the regular solution of the source strong column vector;
calculating the reconstruction error of the surface normal vibration speed of the vibrating body of each equivalent source configuration scheme;
taking the equivalent source configuration scheme with the minimum reconstruction error of the normal vibration speed of the surface of the vibrator as a final equivalent source configuration scheme;
and reconstructing a half-space sound field by using the final equivalent source configuration scheme.
2. The reconstruction method of a half-space sound field according to claim 1, wherein equivalent source configuration is performed according to the position and size of the virtual source surface and the distribution interval of the equivalent sources on the virtual source surface to obtain a plurality of equivalent source configuration schemes.
3. A half-space sound field reconstruction method according to claim 1 or 2, wherein the vibrating body is spherical, and defined as a spherical sound source S, and the equivalent source configuration comprises:
configuring an imaginary source plane gamma as a spherical surface concentric with the spherical sound source S;
configuring the spherical radius of an imaginary source plane gamma;
configuring the distribution of a plurality of equivalent sources of the spherical sound source S on an imaginary source plane gamma;
configuring an imaginary source plane omega as a plane parallel to the reflecting surface;
the retreating distance of the virtual source surface omega relative to the reflecting surface is configured;
configuring the size of a virtual source surface omega;
the distribution of a plurality of equivalent sources characterizing the reflection of the reflecting surface over the imaginary source plane omega is configured.
4. A half-space sound field reconstruction method according to claim 3, wherein when the equivalent source is configured: a plurality of equivalent sources of the spherical sound source S are uniformly distributed on the virtual source plane gamma, and the discrete intervals of the azimuth angle and the polar angle of the equivalent sources on the virtual source plane gamma are pi/4 and pi/6; the size of the virtual source plane Ω is configured, that is, the coordinate range covered by the virtual source plane Ω on the abscissa and the ordinate is configured, and the distribution of the equivalent sources on the virtual source plane Ω is configured, that is, the interval between the equivalent sources in the directions of the abscissa and the ordinate is configured.
5. A reconstruction method of a half-space sound field according to claim 4, characterized in that the size of the virtual source plane Ω and the configuration of the equivalent source distribution are set by the parameter set (x)1,x2,y1,y2,dx,dy) Is represented by the formula (I) in which x1,x2Is the boundary value of the coordinate range covered by the imaginary source plane omega on the abscissa, y1,y2Is the boundary value of the coordinate range covered by the imaginary source plane omega on the ordinate, dx,dyThe discrete distances of the equivalent source on the imaginary source plane omega in the abscissa and ordinate directions.
6. A half-space sound field reconstruction method as claimed in claim 1, wherein two sets of equivalent sources characterizing spherical sound sources and boundary reflection are defined as
Figure FDA0003157766190000021
And
Figure FDA0003157766190000022
wherein
Figure FDA0003157766190000023
And
Figure FDA0003157766190000024
the source strengths of the ith and j equivalent sources respectively;
for any equivalent source configuration scheme, the matrix form of the sound pressure of the half-space sound field of all the measurement points on the holographic surface H is considered as follows:
Figure FDA0003157766190000025
wherein the content of the first and second substances,
Figure FDA0003157766190000026
is a sound pressure transfer function matrix between sound pressure on a representation holographic surface H and an equivalent source on an imaginary source surface gamma,
Figure FDA0003157766190000027
is a sound pressure transfer function matrix between sound pressure on a representation holographic surface H and an equivalent source on an imaginary source surface omega,
Figure FDA0003157766190000028
is a complex acoustic pressure transfer function matrix, QΣIs the source intensity column vector of all equivalent sources, i represents the imaginary unit, ρ represents the air density, and ω represents the angular frequency.
7. The method of claim 6, wherein the source enhancement vector Q isΣThe canonical solution of (a) is:
Figure FDA0003157766190000029
wherein, the superscript "H" represents the Hermite conjugate transpose, the superscript "-1" represents the matrix inversion, ε represents the regularization parameter, and E is the identity matrix.
8. The half-space sound field reconstruction method of claim 7, wherein the surface normal velocity V of the oscillating bodySThe reconstruction is as follows:
Figure FDA0003157766190000031
wherein the content of the first and second substances,
Figure FDA0003157766190000032
the vibration velocity transfer function matrix between the normal vibration velocity on the surface S of the vibration body and equivalent sources on virtual source surfaces gamma and omega is expressed as:
Figure FDA0003157766190000033
in the formula (I), the compound is shown in the specification,
Figure FDA0003157766190000034
consisting of the following functions:
Figure FDA0003157766190000035
Figure FDA0003157766190000036
consisting of the following functions:
Figure FDA0003157766190000037
in the formula, gv,free() Representing the particle velocity transfer function, k is the wave number, ". represents the dot product operation, nSIs the unit normal vector of the surface of the vibrating body,
Figure FDA0003157766190000038
is the nth node of the surface of the vibration body
Figure FDA0003157766190000039
With the ith equivalent source on the imaginary source plane gamma
Figure FDA00031577661900000310
The distance between the two or more of the two or more,
Figure FDA00031577661900000311
is that
Figure FDA00031577661900000312
With the j-th equivalent source on the virtual source plane omega
Figure FDA00031577661900000313
The distance between them;
Figure FDA00031577661900000314
representing equivalent sources
Figure FDA00031577661900000315
To surface node of vibration body
Figure FDA00031577661900000316
The included angle between the straight line transmission direction and the normal direction of the surface of the vibrating body,
Figure FDA00031577661900000317
representing equivalent sources
Figure FDA00031577661900000318
To surface node of vibration body
Figure FDA00031577661900000319
The linear transmission direction of the vibrating body and the normal direction of the surface of the vibrating body form an included angle;
Figure FDA00031577661900000320
are respectively expressed as
Figure FDA00031577661900000321
Figure FDA00031577661900000322
9. The reconstruction method of the half-space sound field according to the claim 1 or 8, wherein for any equivalent source configuration scheme, the reconstruction error of the normal vibration speed of the surface of the vibrating body is as follows:
Figure FDA00031577661900000323
in the formula (I), the compound is shown in the specification,
Figure FDA00031577661900000324
and
Figure FDA00031577661900000325
respectively is the reconstructed normal vibration speed and the theoretical normal vibration speed of the surface of the vibrator; the theoretical normal vibration velocity is expressed as:
Figure FDA0003157766190000041
in the formula, v0Is a uniform radial vibration velocity raIs the radius of the vibrating ball, zSIs the z coordinate of the surface node of the vibrating sphere, zaIs the z coordinate of the center of the sphere.
10. A half-space sound field reconstruction device is characterized by comprising:
the equivalent source configuration module is used for configuring equivalent sources and virtual source surfaces according to the vibrating body and the boundary surface to obtain a plurality of equivalent source configuration schemes; the virtual source surface comprises a virtual source surface gamma where the vibrating body equivalent source is located and a virtual source surface omega where the boundary surface reflection action equivalent source is located;
the source intensity column vector regular solution calculation module is used for calculating the regular solution of the source intensity column vector corresponding to each equivalent source configuration scheme based on the predicted sound pressure of the half-space sound field aiming at each equivalent source configuration scheme;
the vibrating body surface normal vibration velocity calculating module is used for reconstructing the vibrating body surface normal vibration velocity corresponding to each equivalent source configuration scheme based on the regular solution of the source strong column vector;
the reconstruction error calculation module is used for calculating the reconstruction errors of the surface normal vibration speeds of the vibrating bodies of the equivalent source configuration schemes;
the equivalent source configuration scheme selection module is used for taking the equivalent source configuration scheme with the minimum reconstruction error of the normal vibration velocity of the surface of the vibrating body as a final equivalent source configuration scheme;
and the half-space sound field reconstruction module is used for reconstructing the half-space sound field by utilizing the final equivalent source configuration scheme.
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